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Into the Future with Metrology - The Challenges of Digitalization

Tilted-Wave Interferometer (TWI) as Example for Hand-in-Hand Calibration of Real and Virtual Experiments

The optical industry uses aspheres and free-form surfaces in modern optical systems, which, however, place very high demands on metrology. Optical measurement techniques have a prominent role to play here, as they do not damage the measurement objects. The industry urgently needs traceability in optical asphere/free form metrology, which is not yet available with the demanded accuracy. Further research projects can therefore be expected with respect to aspherical and free-form metrology development at the international level.

Current state

The non-contact Tilted-Wave Interferometer (TWI) is used at PTB. With its measuring principle, the optical effect of the measuring system and the object to be measured on wave fronts is recorded by a camera from a large number of directions of incidence. The resulting interference fringe pattern is very complex, and only by simulating the measurement process and solving several inverse problems can the surface shape of the object be deduced. The virtual experiment is part of the modelling of the measurement process. The central objective of PTB is the determination of uncertainty, which is to be determined by combining the virtual experiment with the real measurement setup.

PTB cooperates in the field of tilted-wave interferometry with the University of Stuttgart, where the basic measuring principle was invented, and the company Mahr GmbH, which markets a commercial version of TWI. Internationally, there is cooperation with many NMIs, universities and companies within EMRP/EMPIR projects as well as with the nanotechnology competence center CC UPOB dealing with ultra-precise manufacturing and metrology for surfaces.

Aims and outlook

The further development of the TWI concept is integrated in the "PTB's work and research programme" in topic area 5: Length, dimensional metrology. The project has a particular impact on the promotion of the German and European optical industry and the associated manufacturers of measuring instruments. Aspheres and free-form surfaces are an outstanding future-oriented development in optical systems and have an impact on high-end camera systems, industrial camera systems and also camera applications in the automotive and consumer sectors. The goal of PTB is to achieve a highly accurate, traceable measurement by combining real and virtual experiment. This creates the possibility to trace back industrial measuring technology for optical aspheres and free-form surfaces which enables a much more precise production of such surfaces and will in particular be very positive for the German or European competitiveness.


  1. I. Fortmeier, M. Stavridis, A. Wiegmann, M. Schulz, W. Osten, and C. Elster, “Opens external link in new windowEvaluation of absolute form measurements using a tilted-wave interferometer”, Opt. Express 24, 3393-3404 (2016). 
  2. I. Fortmeier, M. Stavridis, A. Wiegmann, M. Schulz, W. Osten, and C. Elster, "Opens external link in new windowAnalytical Jacobian and its application to tilted-wave interferometry," Opt. Express 22, 21313-21325 (2014).
  3. I. Fortmeier, „Opens external link in new windowZur Optimierung von Auswerteverfahren für Tilted-Wave Interferometer”, Dissertation, Universität Stuttgart, 2016